Divide the following complex numbers: $\dfrac{8(\cos(\frac{23}{12}\pi) + i \sin(\frac{23}{12}\pi))}{4(\cos(\frac{1}{3}\pi) + i \sin(\frac{1}{3}\pi))}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Answer: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $8(\cos(\frac{23}{12}\pi) + i \sin(\frac{23}{12}\pi))$ ) has angle $\frac{23}{12}\pi$ and radius 8. The second number ( $4(\cos(\frac{1}{3}\pi) + i \sin(\frac{1}{3}\pi))$ ) has angle $\frac{1}{3}\pi$ and radius 4. The radius of the result will be $\frac{8}{4}$ , which is 2. The angle of the result is $\frac{23}{12}\pi - \frac{1}{3}\pi = \frac{19}{12}\pi$ The radius of the result is $2$ and the angle of the result is $\frac{19}{12}\pi$.